Question

If the co-ordinates of the middle point of the line segment joining the points (2, 1) and (1,
-3) be (a, b), show that 6a + b -8 = 0.

Answer 1

Answer:

Co-ordinates if the mid-point of AB = (3/2 , -1)

Step-by-step explanation:

Given,

A = (2 , 1)

B = (1 , -3)

Co-ordinate of the mid-point AB = (a , b).

To Find :-

1) The co-ordinate of the mid-point

2) To Prove :- 6a + b - 8 = 0

How To Do :-

Here they given the values of co-ordinates of point 'A' and point 'B and asked us to find the value of co-ordinates of the mid-point of line segment AB. So we need to find the value of the mid-point by substituting the co-ordinates in the mid-point formula. After by comparing that co-ordinates with (a , b) we can obtain the value of 'a' and 'b' and we need to prove that '6a + b - 8 = 0'.

Formula Required :-

Mid-point formula :-

$Mid-point=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Solution :-

Mid-point :-

$=\left(\dfrac{2+1}{2},\dfrac{1-3}{2}\right)$

= (3/2 , -2/2)

= (3/2 , -1)

∴ Co-ordinates if the mid-point of AB = (3/2 , -1)

→ (3/2 , -1)  = (a , b)

By comparing :-

a = 3/2

b = -1

6a + b - 8 = 0

Taking L.H.S :-

= 6a + b - 8

Substituting the values :-

= 6(3/2) + (-1) - 8

= 3(3) - 1 - 8

= 9 - 9

= 0

= R.H.S

∴ Proved that '6a + b - 8 = 0'

Answer 2

Given :- the co-ordinates of the middle point of the line segment joining the points (2, 1) and (1,-3) be (a, b), show that 6a + b -8 = 0.

Solution :-

we know that, coordinates of mid points of X(a,b) and Y(c,d) is :-

• x = (a + c)/2
• y = (b + d)/2

given that, ordinates of the middle point of the line segment joining the points (2, 1) and (1,-3) be (a, b) .

so,

→ a = (2 + 1)/2

→ a = (3/2)

and,

→ b = (1 - 3)/2

→ b = (-2)/2

→ b = (-1)

then, putting these values in given equation,

→ 6a + b - 8 = 0

→ 6 * (3/2) + (-1) - 8 = 0

→ 3 * 3 - 1 - 8 = 0

→ 9 - 9 = 0

→ 0 = 0

→ LHS = RHS (Proved) .

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